Method and apparatus for processing audio and speech signals

ABSTRACT

A method and device for processing signals representing speech or audio via a plurality of filters that approximate behaviors of the basilar membrane of human cochlea. Each of the plurality of filters is formed from a mother filter via the dilation and a shift in time and has the similar impulse response of the basilar membrane to the frequency band for which the filter represents. Any process can be conducted and any feature can be extracted in the domain of the filters&#39; outputs for applications, such as noise reduction, speech synthesis, coding, and speech and speaker recognition. Processed signals can be synthesized back to the time domain via an inverse cochlear transform

FIELD OF THE INVENTION

The present invention is generally directed to a method and apparatusfor processing audio and speech signals. In particular, the presentinvention is directed to a method and apparatus for processing audiosignals representing, e.g., human speech, music, and background noise,via a cochlear filter bank that mimics the response of the basilarmembrane in the cochlea to pure tones of different frequency bands.

BACKGROUND INFORMATION

Human speeches may be captured as signals representing speech or speechsignals using transducers, e.g., microphones, and be further processedfor a wide range of applications, e.g., noise reduction or denoising,speech recognition, speaker recognition, speech synthesis, hearing aids,cochlear implants, and speech compression. The speech signals may becaptured in the form of analog signals or digital signals and may bestored in electronic media, e.g., memory or disks. The speech signalsmay be processed using analog or digital processors.

One commonly used scheme in speech signal processing may includetransforming speech signals from a time domain representation, e.g.,signal waveforms as a function of time, into a frequency domainrepresentation, e.g., spectrums or spectrograms, using the Fouriertransformation. However, the Fourier transform may have a fixedtime-frequency resolution. Thus, frequency distribution is limited to alinear scale. This limitation may require additional processing, e.g.,converting a linear frequency distribution to a non-linear frequencydistribution, e.g., as in the basilar membrane. Additionally, the fixedwindow size of the Fourier transform may cause undesirable harmonics inspectrograms.

This problem may be illustrated by the following example. In most speechprocessing systems, speech signals are first converted into digitalsignals on which, for example, short-time Fourier transform via FastFourier Transforms (FFT) may be applied for computing spectrograms ofthe speech signals. The intensity of a spectrogram represents theamplitude of the signal at a particular time and at a particularfrequency. FIG. 1 shows speech signals of a male voice recorded undertwo different scenarios. FIG. 1(A) shows the speech signal recordedusing a close-talking microphone, and FIG. 1(B) shows the same speechsignal simultaneously recorded using a hands-free microphone in a movingvehicle. The close-talking microphone is placed near the speaker'smouth, while the hands-free microphone is placed, e.g., on a sun visorof the vehicle. Due to the distance between the mouth and the microphonein the hands-free scenario, the recorded speech signal in FIG. 1(B) mayinclude substantial background noise compared to the speech signal asshown in FIG. 1(A). Both speech signals in this example are recorded ata sampling rate of 8 KHz.

FIG. 2 shows the spectrograms of speech signals shown in FIG. 1.Specifically, FIG. 2(A) shows a spectrogram of the clean speech signalrecorded using a close-talking microphone as shown in FIG. 1(A), andFIG. 2(B) shows a spectrogram of the noisy speech signal recorded usinga hand-free microphone as shown in FIG. 1(B). The spectrograms arecomputed in the standard way, as in traditional feature extraction forspeaker or speech recognition. It may include using a window of, e.g.,the length of 30 ms shifted every 10 ms with an overlap of 20 ms, of atype of Hamming window before applying FFT to the speech signals. Tofacilitate further analysis and feature extraction, the frequencydistribution is mapped from linear scales to the Bark scale after theFFT computation.

The spectrograms of FIG. 2 shows two types of distortions: (1) the pitchharmonics as periodical waves along the frequency axis; and (2) thebackground noise in the frequency domain in the form of “snow” noise(which is different from environmental noise). Both types of distortionsare caused by FFT computation.

Additional processing steps may be needed to remove effects of theseundesirable distortions. FIG. 3 shows a schematic diagrams of such aFourier transform based system 300 for extracting features from speechsignals. A speech signal may first undergo pre-processing steps of frameblocking 302 and windowing 304. Then at 306 FFT may be applied to thepre-processed speech signal for computing a spectrum. As discussedabove, the spectrum may include unwanted harmonics and noise. In thismethod, triangular filters 308, a non-linear filter 310, and discretecosine transform (DCT) 312 may be applied to reduce the effects ofharmonics and noises caused by FFT. However, while these steps mayreduce the harmonic distortions, they may also remove useful and realpitch information. It is commonly known that humans identify peoples'voices by the voice characteristics, represented mainly by pitchinformation.

Speech signal processing based on wavelet transforms may provideflexible time-frequency resolution. However, it may have othernoticeable problems. First, the existing wavelet does not have thecapabilities of mimicking the impulse responses of the basilar membrane.Thereby, it may not be used directly for modeling the human hearingsystem, e.g., cochlea. Second, there is no discrete formula toapproximate inverse continuous wavelet transforms even though forwardand inverse transforms for continuous wavelet based are well defined.

SUMMARY OF INVENTION

Due to the limitation of FFT computation, the pitch information of humanspeech has not been fully utilized in speech signal processing, andharmonic distortions may be added in the computation. Thus, there is aneed for a speech signal processing method that causes less harmonicdistortions and does not require additional computations to rectifyharmonic distortions.

One example embodiment of the present invention includes a speech signalprocessing method or apparatus that takes into account thecharacteristics of human voice and hearing system to reduce the unwantedharmonic distortions. Referring to FIG. 4, the human hearing system mayinclude an outer (external) ear, a middle ear, and an inner ear. Soundwaves may go through the outer ear and push on to the eardrum. Theeardrum and three middle ear bones may work together as a mechanicalamplifier and transfer the sound waves through movements of the bones.The last bone of the three may be connected to a cochlea, which may befilled with liquid and have a basilar membrane in the middle.

FIG. 5 shows a stretched-out cochlea. The movement of the last bonegenerates a traveling wave. The traveling wave may have the highestresponse at the location corresponding to a pure tone at a specificfrequency. The frequency distribution on the basilar membrane may be ina nonlinear Bark, ERB (equivalent rectangular bandwidth), or Log scale.The hair cells connected to the basilar membrane may convert themovement of the traveling wave into electrical signals and transmit thesignals to the human brain.

In one example embodiment of the present invention, a speech signal maybe processed via a filter bank whose response mimics that of a cochleato a pure tone (called “cochlear transformation” or CT hereafter). TheCT may convert speech signals from time domain into a cochlear frequencydomain representation. The spectrum of speech signals in the cochlearfrequency domain may have much reduced harmonic distortions and noisecaused by FFT. The speech signals may be further processed based on therepresentation in the CT domain. The processed speech signals may thenbe transformed back to time domain based on an inverse cochleartransform (ICT).

In one example embodiment of the present invention, the CT may modeltraveling waves on the basilar membrane in the human cochlea. The outputfrom a CT may represent the traveling waves of, e.g., speech signals, onthe basilar membrane in decomposed frequency bands. A further ICT mayconvert the traveling waves back to the original signal. In one exampleembodiment of the present invention, a discrete-time CT may beformulated for converting digitized speech signals into digitaltraveling waves. Correspondingly, a discrete-time ICT may be formulatedfor converting the digital traveling waves back into digitized speechsignals.

In one example embodiment of the present invention where a speech signal(or an audio signal, or a music signal) includes background noise, thespeech signal may be transformed based on the CT into a number offrequency bands. Noise on each frequency band may then be detected. Forexample, the energy and spectral patterns of the background noise iscommonly different from foreground speech or music signals. Noise may bedetected by comparing the spectrum of noise against the spectrum ofspeech or music. After the detection, a linear or nonlinear threshold,gain, or filter can be applied to the speech signal to reduce or removecomponents corresponding to noise while keeping or enhancing componentscorresponding to the speech, music, or audio signals. The processedmulti-band signals can be synthesized based on an ICT back to a cleanedsignal with improved signal to noise ratio.

In another example embodiment of the present invention in theapplication field of speech and music synthesis, a speech or musicsignal may be converted to components within different frequency bandsusing CT. A plurality of samples of the speech signal within each bandmay then be removed or replaced based on pre-trained multiple-bandmodels. The processed multi-band signals can be synthesized based on anICT back to a time domain signal. The synthesized speech signal mayinclude a change (shorter or longer) of speech duration with the effectsof, e.g., slower or faster talk than the original speech signal.

In yet another example embodiment of the present invention in theapplication field of speech or speaker recognition, as shown in FIG. 13,a CT 1302 decomposes a speech (or audio) signal into frequency bands atsubstantially the same frequency scales as in a basilar membrane. Aspeech feature extractor may then be used to extract speech featuresfrom each frequency band through linear or nonlinear operations. Forexample, as shown in FIG. 13, for each time instance, the magnitudevalues computed for each frequency band may be weighted differently soas to achieve equal loudness at 1308, where the loudness may be aquality of sound that is related to its magnitude. A nonlinearprocessing 1304 may be applied after a CT transform to limit the outputof each of the CT bands, y_(i), to a range, where i is the band number.In one example embodiment, only the positive value for y_(i) are keptand the negative value are reset to zero. In an alternative exampleembodiment, the nonlinear processing 1304 may be bypassed. The output ofthe nonlinear filter may then be used to calculate energy for aspectrogram at 1306. The energy or absolute value may be a windowedaverage with a window size of 2-4 periods of the central frequency ofthe specific frequency band or alternatively with windows of a fixedsize. Moreover, the windows may have been generated from a slidingwindow. At 1314, the output of the windowed average energy functionalitymay be scaled, e.g., by a cubic root operation. After a Discrete CosineTransform (DCT) 1310, the output of the feature extractor may be asequence of feature vectors, e.g., cepstrum or delta-cestrum (i.e.,temporal derivative of cepstrum), for a speech recognition or speakerrecognition engine.

In yet another example embodiment of the present invention in theapplication field of hearing aid, speech signals may be processed via CTon the hearing aid for sound amplification, noise reduction,equalization, and localization. Each of these functionalities may beimplemented in each of the frequency band adapted to the user's need.The processed multi-band signals may be synthesized into one-channelsound signal to a transducer, e.g., a speaker, in the ear.

In yet another example embodiment of the present invention in theapplication field of audio compression or coding, an audio signal may bedecomposed via a CT into different frequency bands. The signal at lowerfrequency bands may be down-sampled, on which a sub-band codingtechnique may then be applied for coding or data compression. Encodedsignals may also be decoded into the multiple-band signal and then beconverted back to signals that are substantially approximate to theoriginal signals by the synthesis.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1(A)-(B) show speech signal waveforms of a male voicesimultaneously recorded by (A) a close-talking microphone and (B) by ahands-free microphone, in a moving vehicle.

FIGS. 2(A)-(B) show the corresponding spectrograms of the speech signalsas shown in FIGS. 1A-1B using FFT and displayed in Bark scales from 0 to6.4 Barks (0 to 3500 KHz).

FIG. 3 shows a conventional Fourier transform based speech signalprocessing system for extracting speech features.

FIG. 4 shows an illustration of components of a human ear.

FIG. 5 shows a stretched-out cochlea and the cross-section of thebasilar membrane inside the cochlea with a traveling wave along apropagation direction.

FIG. 6 shows example impulse responses of CT base functions similar to aresponse of BM to a pure tone according to one example embodiment of thepresent invention.

FIGS. 7(A)-(B) show two example cochlear filter banks according to oneexample embodiment of the present invention.

FIG. 8 shows an example speech processing system based on adiscrete-time cochlear transform according to one example embodiment ofthe present invention.

FIG. 9 shows an example speech recognition system based on adiscrete-time cochlear transformation according to one exampleembodiment of the present invention.

FIG. 10 shows an example signal processing system based on a continuouscochlear transform according to one example embodiment of the presentinvention.

FIGS. 11(A)-(B) show the corresponding spectrograms of the speechsignals as shown in FIGS. 1A-1B using the CT and displayed in Barkscales from 0 to 6.4 Barks (0 to 3500 KHz).

FIG. 12(A) shows a spectrum at time 1.15 second of the spectrograms (CC′cross-section) shown in FIGS. 11(A)-(B) with the solid linecorresponding to the close-talking microphone recording and thedashed-line corresponding to the hands-free microphone recording.

FIG. 12(B) shows a spectrum at time 1.15 second of the spectrograms (CC′cross-section) shown in FIGS. 2(A)-(B) with the solid line correspondingto the close-talking microphone recording and the dashed-linecorresponding to the hands-free microphone recording.

FIG. 13 shows a speech feature extraction system based on the CTaccording to one example embodiment of the present invention.

DETAILED DESCRIPTION OF EXAMPLE EMBODIMENTS

In one example embodiment of the present invention, a cochlear transformmay be based on a base function that mimics a response of human basilarmembrane (BM) in human cochlea to a pure tone. Such a function, ψ(t) εL²(R), may be characterized by following conditions: (1) it integratesto zero:

∫_(−∞)^(∞)ψ(t)t = 0;

(2) it is square integrable with finite energy:

∫_(−∞)^(∞)ψ(t)²t < ∞;

(3) it satisfies

${{\int_{- \infty}^{\infty}{\frac{{{\psi (\omega)}}^{2}}{\omega}{\omega}}} = C},$

where C, 0<C<∞, is a constant; (4) a plot of ψ(t) follows observationsof characteristic of BM in psychoacoustic experiments and tapers off tozero on both ends; and (5) the ψ(t) has one major modulation frequencyand its frequency response is a triangle-like, band-pass filter centeredat the modulation frequency. Conditions (4) and (5) are specificallydesigned to reflect experimental results from previous psychoacousticand physiological experiments. FIG. 6 shows example impulse responses ofCT base functions similar to a response of BM to a pure tone accordingto one example embodiment of the present invention.

A cochlear transformation may be constructed from the base function. Fora given a square integrable signal, e.g., a speech signal, f(t), a CTmay transform f(t) based on the base function ψ(t):

${T\left( {a,b} \right)} = {\int_{- \infty}^{\infty}{{f(t)}\frac{1}{\sqrt{a}}{\psi \left( \frac{t - b}{a} \right)}{t}}}$

where a and b are both real numbers, and both f(t) and ψ(t) aresquare-integrable (or belong to L²(R) space), and T(a, b) representstraveling waves in the BM. The 1/√{square root over (|a|)} is an energynormalization factor that ensures the total energy, or

${\int_{- \infty}^{\infty}{{{\psi \left( \frac{t - b}{a} \right)}}^{2}{t}}},$

stays substantially the same for all a and b. The factor a may representa scale or dilation variable. A change in dilation a may shift thecentral frequency of the impulse response of ψ(t). The factor b may be atime shift or translation variable. For a given dilation a, the shift bmay shift the function

${\psi_{a,b}(t)} = {\psi \left( \frac{t - b}{a} \right)}$

by an amount b along the time axis. We call ψ_(a,b)(t) the cochlearfunction or cochlear filter.

In one example embodiment of the present invention, the cochlearfunction may be formulated as

${\psi_{a,b}(t)} = {\frac{1}{\sqrt{a}}\left( \frac{t - b}{a} \right)^{\alpha}{\exp \left\lbrack {{- 2}\; \pi \; f_{L}{\beta \left( \frac{t - b}{a} \right)}} \right\rbrack}{\cos \left\lbrack {{2\; \pi \; {f_{L}\left( \frac{t - b}{a} \right)}} + \theta} \right\rbrack}{u(t)}}$

where α>0 of value, e.g., 3, and β>0 of value, e.g., 0.035, u(t) is anunit step function, i.e., u(t)=1 for t≧0 and 0 otherwise. The parametersof ψ_(a,b)(t), e.g., θ, are chosen such that the above-discussed fiveconditions are satisfied. The value of a may be determined by a centralfrequency f_(c) of the current filter and the lowest central frequencyf_(L) in a cochlear filter bank such that a=f_(L)/f_(c). For differentvalues of (a, b), ψ_(a,b)(t) may represent different filters within afilter bank. When 0<a≦1, the filter is contracted in scale along thetime axis. When a>1, the filter is expanded in scale along the timeaxis. For different values of a, e.g., as, i=1, . . . , n, correspondingcentral frequencies f_(ci) may be pre-computed for each filter. FIG. 7shows two example filter banks in the frequency domain. FIG. 7(A) showsfilters with larger values of b=0.2 so that each filter is stretchedout, while FIG. 7(B) shows filters with smaller values of b=0.035_(i) sothat each filter is narrow. The distribution of cochlear filters in thefrequency domain may be according to linear or nonlinear scales, e.g.,ERB (equivalent rectangular bandwidth), Bark, log, or any other scalesbased on the requirements from real world practices.

In one example embodiment of the present invention, a CT may have acorresponding ICT that may transform a time frequency representation,e.g., T(a, b), back to time domain:

${f(t)} = {\frac{1}{C}{\int_{a = 0}^{\infty}{\int_{b = 0}^{\infty}{\frac{1}{{a}^{2}}{T\left( {a,b} \right)}{\psi_{a,b}(t)}{a}{{b}.}}}}}$

In another example embodiment of the present invention, a discrete-timecochlear transform may be applied to digitized signals, e.g., speechsignals. For a digitized signal, f[n], n=1, . . . N, where N is thelength of the signal, the discrete-time cochlear transform is

${T\left\lbrack {a_{i},b} \right\rbrack} = {\sum\limits_{n = 0}^{N}{{f\lbrack n\rbrack}\frac{1}{\sqrt{a_{i}}}{\psi \left\lbrack \frac{n - b}{a_{i}} \right\rbrack}}}$

where a_(i)=f_(L)/f_(c) _(i) is the scaling factor for the ith frequencyband with central frequencies f_(c) _(i) . The scaling factor a_(i) maybe linear or nonlinear scales. Similar to continuous cochlear transform,for discrete-time cochlear transform, a_(i) may be in ERB, Bark, log, orother nonlinear scales.

Correspondingly, discrete-time cochlear transform may have an inversediscrete-time cochlear transform:

${\overset{\_}{f}\lbrack n\rbrack} = {\frac{1}{C}{\sum\limits_{a_{i} = a_{1}}^{a_{k}}{\sum\limits_{b = 1}^{N}{\frac{1}{a_{i}}{T\left\lbrack {a_{i},b} \right\rbrack}{\psi \left\lbrack \frac{n - b}{a_{i}} \right\rbrack}}}}}$

where 0≦n≦N, a₁≦a_(i)≦a_(k), and 1≦b≦N. The f[n] is substantiallyapproximate to f[n] when the number of frequency bands is limited.

Fast calculations of the discrete-time cochlear transform and inversediscrete-time cochlear transform may be implemented in manners similarto FFT. In addition, the resolution of lower frequency bands may bereduced to further improve computation speed.

FIG. 8 shows an example speech processing system based on adiscrete-time cochlear transform according to one example embodiment ofthe present invention. Analog signal waveforms, e.g., human speech, maybe first provided to an analog to digital converter (ADC) 802 forconverting analog signal waveforms into digital signal waveforms. Aprocessor 804, e.g., a DSP, a CPU, or any type of suitable processor,may execute codes that are stored in a storage media 808, e.g., a memoryor a hard drive. The execution of the codes stored in the media 808 mayperform CT based signal processing methods. According to one exampleembodiment of the present invention, the digital signal waveforms mayfirst, at 810, convolute with filters in a cochlear filter bank, or inanother word, undergo a discrete-time cochlear transform. Then at 812,the digital signal may be further processed based on its frequencydomain representation. In one embodiment of the present invention, noisein the speech signal may be removed with filters on different frequencybands. In another embodiment of the present invention, some frames orvectors of the filter bank outputs may be selected and removed to makethe speed of speech faster. At 814, an inverse discrete-time cochleartransform may be applied to the output of the digital signal processingunit 812 to produce processed digital signal waveforms. The processeddigital signal waveforms may then be converted back to analog signalusing a digital to analog converter (DAC) 806. The processed analogsignal may be, e.g., cleaned speech or enhance audio signal.

FIG. 9 shows an example speech recognition system based on adiscrete-time cochlear transformation according to one exampleembodiment of the present invention.

Human speech may be recorded using a transducer, e.g., a microphone 902,as analog speech signals. The analog speech signals may then beconverted into digital speech signals via a ADC 904. Using the digitalspeech signals as an input, a processor 906 may execute codes stored ina storage medium 908 to perform following steps. First, a discrete-timecochlear transform 910 may be applied to the digital speech signals viaa cochlear filter bank to transform the digital speech signals into afrequency or time-frequency domain representation, e.g., a spectrum orspectrogram of the speech signals. Based on the frequency domainrepresentation, speech features may be extracted at 912 using, e.g., theapproach depicted in FIG. 13. Further, a speech recognizer 914 mayconvert the speech feature frames/vectors into text. The speechrecognizer 914 may be any conventional speech recognizer. Alternatively,for speaker recognition applications, the module 914 may be a speakerrecognizer that identifies speakers based on speech.

FIG. 10 shows an example signal processing system based on a continuouscochlear transform according to one example embodiment of the presentinvention. Analog signals may first be filtered through an analogcochlear filter bank of central frequencies f_(c) _(i) that may bedistributed according to, e.g., Bark scales. The analog cochlear filtersmay be construct from analog components as known to a skilled artisan. Asignal processing unit may then process the decomposed signals at, e.g.,different frequency bands. One example of processing may remove orreduce noise according to locations of frequency bands. Another examplemay involve sub-sampling for a change of the speech characteristics orspeed. The processed analog signals may then be synthesized based on anICT filters bank. Similarly, these synthesizers may be made from analogcomponents.

Experimental results show that the CT-based signal processing approachproduce superior results compared to FFT-based approaches. FIGS.11(A)-(B) show the corresponding spectrograms of the speech signals asshown in FIGS. 1A-1B using CT and displayed in Bark scales from 0 to16.4 Barks (0 to 3500 KHz). Compared to the spectrograms produced usingFFT as shown in FIGS. 2(A)-(B), the CT spectrograms have significantlyless noise caused by FFT computations and almost no pitch harmonics.FIG. 12(A) shows a CT spectrum at time 1.15 second of the spectrograms(CC′ cross-section) shown in FIGS. 11(A)-(B) with the solid linecorresponding to the close-talking microphone recording and thedashed-line corresponding to the hands-free microphone recording. FIG.12(B) shows an FFT spectrum at time 1.15 second of the spectrograms (CC′cross-section) shown in FIGS. 2(A)-(B) with the solid line correspondingto the close-talking microphone recording and the dashed-linecorresponding to the hands-free microphone recording. Compared with theFFT spectrum shown in FIG. 12(B), first the CT spectrum shown in FIG.12(A) contains much less pitch harmonic distortions. The pitch harmonicsin the FFT spectrum, as shown in FIG. 12(B), are artificial noisescaused by the computation via FFT. The processing based on CT may avoidthe drawbacks of FFT by emulating the behavior of basilar membrane in ahuman hearing system. Second, FIG. 12(B) shows a substantial distortionof approximately 30 dB on the FFT spectrum at the far left side due tocar noise. By comparison, the difference is much smaller for CTspectrum. This improvement may provide the potential to develop newfeatures for speech and speaker recognition. Last, the FFT spectrum maynot be used as the feature for speaker recognition directly and mayrequire triangular filters and discrete cosine transform to furtherremove the effect of the pitch harmonics. As a result, the importantpitch information and the pitch harmonics may be removed altogether.This is one of the reasons that pitch information has yet to be used inspeaker recognition.

Those skilled in the art may appreciate from the foregoing descriptionthat the present invention may be implemented in a variety of forms, andthat the various embodiments may be implemented alone or in combination,in hardware or software, and in analogue or digital circuits. Therefore,while the embodiments of the present invention have been described inconnection with particular examples thereof, the true scope of theembodiments and/or methods of the present invention should not be solimited since other modifications will become apparent to the skilledpractitioner upon a study of the drawings, specification, and followingclaims.

1. A method for processing signals representing a speech via a pluralityof filters that approximate behaviors of basilar membrane in humancochlea, comprising: providing a first signal representing speech oraudio to the plurality of filters; and filtering the first signal withthe plurality of filters, each of the plurality of filters producing oneof a plurality of filtered signals; wherein each of the plurality offilters is formed from a mother filter via a dilation and a shift intime; and an impulse response of the mother filter is substantiallysimilar to an impulse response of the basilar membrane in the humancochlea to a pure tone.
 2. The method of claim 1, wherein: the signal isa digital signal representing speech or audio, the mother filter is adigital filter representing the impulse response at a point on thebasilar membrane to a corresponding frequency, and the each of theplurality of filters is a digital filter formed from the mother filtervia a dilation and a shift in time.
 3. The method of claim 2, whereineach of the plurality of digital filters has a frequency response towhich a central frequency is associated.
 4. The method of claim 3,wherein central frequencies to the plurality of digital filters aredistributed according to one of a Bark scale, an equivalent rectangularbandwidth (ERB) scale, and a log scale.
 5. The method of claim 2,wherein the signal is filtered according to${{T\left\lbrack {a_{i},b} \right\rbrack} = {\sum\limits_{n = 0}^{N}{{f\lbrack n\rbrack}\frac{1}{\sqrt{a_{i}}}{\psi \left\lbrack \frac{n - b}{a_{i}} \right\rbrack}}}},$wherein for the shift of b and a dilation of a_(i), the each of theplurality of digital filters is determined according to${{\psi_{a_{i},b}(n)} = {\frac{1}{\sqrt{a_{i}}}\left( \frac{n - b}{a_{i}} \right)^{\alpha}{\exp \left\lbrack {{- 2}\; \pi \; f_{L}{\beta \left( \frac{n - b}{a} \right)}} \right\rbrack}{\cos \left\lbrack {{2\; \pi \; {f_{L}\left( \frac{n - b}{a_{i}} \right)}} + \theta} \right\rbrack}{u(n)}}},$wherein n=1, . . . , N, are discrete time instances, u(n) is a stepfunction, and α, β, θ, and f_(L) are constants.
 6. The method of claim5, wherein the a is in a range of 1 to 4 and the β is in a range of 0.01to 0.5.
 7. The method of claim 5, wherein thee is substantiallyapproximate to a value of 3 and the β is substantially approximate to avalue of 0.035.
 8. The method of claim 5, further comprising: processingthe plurality of the filtered signals according a set of pre-determinedrules to produce a plurality of processed signals; and synthesizing asecond speech signal based on a summation of products of each of theprocessed the plurality of the filtered signals and each of theplurality of filters.
 9. The method of claim 8, wherein the processingincludes at least one of a reduction of noise in the speech or audio, achange of magnitude of the digital signal, and a change of number oftimes frames in the digital signal at the output of CT.
 10. The methodof claim 8, wherein the synthesizing the second speech signal is basedon:${\overset{\_}{f}\lbrack n\rbrack} = {\frac{1}{C}{\sum\limits_{a_{i} = a_{1}}^{a_{k}}{\sum\limits_{b = 1}^{N}{\frac{1}{a_{i}}{\overset{\_}{T}\left\lbrack {a_{i},b} \right\rbrack}{\psi \left\lbrack \frac{n - b}{a_{i}} \right\rbrack}}}}}$wherein 0≦n≦N, a₁≦a_(i)≦a_(k), and 1≦b≦N, T[a_(i),b] represents theplurality of the filtered signals with the shift of b and a dilation ofa_(i), and $\psi \left\lbrack \frac{n - b}{a_{i}} \right\rbrack$represents the function for the plurality of filters.
 11. The method ofclaim 2, further comprising: extracting at least one feature from thefiltered signal for a speech recognition application.
 12. The method ofclaim 11, wherein the at least one feature includes CT cepstralcoefficients.
 13. The method of claim 2, wherein: the signal is ananalog signal representing speech or audio, the mother filter is ananalog filter denoting a continuous waveform, and the each of theplurality of filters is an analog filter formed from the mother filtervia a dilation and shift in time.
 14. The method of claim 13, whereinthe each of the plurality of filters is made from analog components. 15.A machine-readable storage media having stored thereon instructionsadapted to be executed by a processor to perform a method for processingsignals representing a speech via a plurality of filters thatapproximate behaviors of human cochlea, comprising: providing a firstsignal representing speech to the plurality of filters; and filteringthe first signal with the plurality of filters, each of the plurality offilters producing one of a plurality of filtered signals; wherein eachof the plurality of filters is formed from a mother filter via adilation and a shift in time; and an impulse response of the motherfilter is substantially similar to an impulse response of a basilarmembrane in the human cochlea to a sound.
 16. A system for processingsignals representing a speech via a plurality of filters thatapproximate behaviors of human cochlea, comprising: a plurality offilters; and a processor configured to: providing a first signalrepresenting speech to the plurality of filters; and filtering the firstsignal with the plurality of filters, each of the plurality of filtersproducing one of a plurality of filtered signals; wherein each of theplurality of filters is formed from a mother filter via a dilation and ashift in time; and an impulse response of the mother filter issubstantially similar to an impulse response of a basilar membrane inthe human cochlea to a pure tone sound.